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3 years ago

Help me out pleaseee

Mathematics

1 answer:

spayn [35]3 years ago

8 0

Answer:

Option B is the correct choice.

Step-by-step explanation:

The graph is attached below.

We have to find the $x$ intercept meaning the value of the point on $x-axis$ when $y=0$

So we will put the value of zero $(0)$ instead of $y$ in our given equation.

So here we have solved it algebraically.

$y=\frac{3}{4}x-3$

Putting $y=0$

$0=\frac{3}{4}x-3$

$0=\frac{3x-12}{4}$

Multiplying $4$ both sides.

$0=3x-12$

Adding $12$ both sides.

$12=3x$

Dividing with $3$ both sides.

$x=\frac{12}{3}=4$

So the x-intercept of the given equation is $4$ which can be written as $(4,0)$ in terms of coordinates.

Option B $(4,0)$ is the correct choice.

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Suppose a batch of metal shafts produced in a manufacturing company have a population standard deviation of 1.3 and a mean diame

lbvjy [14]

Answer:

54.86% probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 208, \sigma = 1.3, n = 60, s = \frac{1.3}{\sqrt{60}} = 0.1678$

What is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.1 inches

Lesser than 208 - 0.1 = 207.9 or greater than 208 + 0.1 = 208.1. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Lesser than 207.9.

pvalue of Z when X = 207.9. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{207.9 - 208}{0.1678}$